- #1
lrhorer
- 22
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There are several threads on the Bell paradox, plus the article in the FAQ forum, but I must be missing something here.
Forget for a moment about 2 ships. Let's take one ship, which an observer at the front and the other at the rear. The ship is undergoing a constant 1G acceleration. The conclusion from the proposed paradox would seem to be the compressive stress in the skin of the ship is less than 1G, and that at some point in time it may actually fall to zero and even eventually become an expansive stress and perhaps even grow so large that the ship is ripped apart. I don't see how that would be possible, since at any point in time both observes and the ship itself are all at rest WRT each other, irrespective of the ships motion wrt any external frame of reference. As I say, I'm missing something, here. Someone please explain.
Meanwhile, let's return to the two ship scenario.
We have two identical ships, pined in the same direction, a few hundred meters or so apart. Ship 1 begins accelerating toward ship 2 at time t1, so that an observer in the ship feels a constant 1G acceleration. Ship 2 begins accelerating at time t2, away from ship 1. Clearly there are an infinite number of values of t1 and t2 that will allow ship 1 to overtake ship 2. There are likewise an infinite number of values of t1 and t2 that will cause ship 2 to out-distance ship 1. The proposed paradox is suggesting, however, there are no values for t1 and t2 that would ever allow the two ships to remain motionless wrt each other. Again, someone please explain this to me.
OK, now to the really fun stuff. In stead of rockets, let's talk about a circular disk. The disk has a small mass, but infinitely strong, so it won't fly apart. It is not, however, rigid. It can be deformed under stress. There is a straight painted along a diameter of the disk. We start spinning the disk with a constant angular acceleration measured at the edge of the disk. The straight line takes on a very slight curve shaped rather like an S. At normal velocities the shape of the curve does change radically as the disk's rotational velocity increases, because that the disk grows larger in diameter with each passing second, and because the torque required to maintain the angular acceleration increases. Nonetheless, the angular velocity of the edge of the disk is the same as that toward the center at any given time, and the curve is only changing slightly with time. The question: What happens as the outer edge of the disk approaches the speed of light? What happens to the curved line?
Forget for a moment about 2 ships. Let's take one ship, which an observer at the front and the other at the rear. The ship is undergoing a constant 1G acceleration. The conclusion from the proposed paradox would seem to be the compressive stress in the skin of the ship is less than 1G, and that at some point in time it may actually fall to zero and even eventually become an expansive stress and perhaps even grow so large that the ship is ripped apart. I don't see how that would be possible, since at any point in time both observes and the ship itself are all at rest WRT each other, irrespective of the ships motion wrt any external frame of reference. As I say, I'm missing something, here. Someone please explain.
Meanwhile, let's return to the two ship scenario.
We have two identical ships, pined in the same direction, a few hundred meters or so apart. Ship 1 begins accelerating toward ship 2 at time t1, so that an observer in the ship feels a constant 1G acceleration. Ship 2 begins accelerating at time t2, away from ship 1. Clearly there are an infinite number of values of t1 and t2 that will allow ship 1 to overtake ship 2. There are likewise an infinite number of values of t1 and t2 that will cause ship 2 to out-distance ship 1. The proposed paradox is suggesting, however, there are no values for t1 and t2 that would ever allow the two ships to remain motionless wrt each other. Again, someone please explain this to me.
OK, now to the really fun stuff. In stead of rockets, let's talk about a circular disk. The disk has a small mass, but infinitely strong, so it won't fly apart. It is not, however, rigid. It can be deformed under stress. There is a straight painted along a diameter of the disk. We start spinning the disk with a constant angular acceleration measured at the edge of the disk. The straight line takes on a very slight curve shaped rather like an S. At normal velocities the shape of the curve does change radically as the disk's rotational velocity increases, because that the disk grows larger in diameter with each passing second, and because the torque required to maintain the angular acceleration increases. Nonetheless, the angular velocity of the edge of the disk is the same as that toward the center at any given time, and the curve is only changing slightly with time. The question: What happens as the outer edge of the disk approaches the speed of light? What happens to the curved line?